It is known that a consumer buys two goods, the amounts of which are x and y. Her marginal utility of consuming good x is U x , while that of...

It is known that a consumer buys two goods, the amounts of which are x and y. Her marginal utility of consuming good x is Ux , while that of consuming good y is Uy. If the two marginal utility functions are given by

Ux = 8y + x2 and Uy =2x  and the consumer is known to stay on the same utility curve, find the total utility function of this consumer buying the two goods.(Hint: Since the consumer stays on the same utility curve Uxdx+ Uydy = 0.)